Fishtank Learning

6th Grade Math
Unit 8: Statistics
Lesson 9

Objective

Use the range and interquartile range to understand the spread and variability of a data set.

Anchor Problems - Problem 1

Recall the Anchor Problem you worked with from Lesson 6 of this unit, about the temperatures in March.

For Paper Strip A: Temperatures of the first 11 days in March
24 35 64 60 35 21 31 38 49 57 50

For Paper Strip B: Predicted temperatures of the last 10 days in March
50 49 49 49 49 48 48 46 46 48

a. Refold each paper strip in half so that half of the temperatures are on the left side and half of the temperatures are on the right side. What data point did you just find?

b. Fold each half of the strips in half again to create fourths or quarters. What percent or fraction of the data set is represented in each section of the strip?

c. Define and name the lower quartile, median, and upper quartile temperatures for the first 11 days of March and the last 10 days of March.

d. Find the range and interquartile range of temperatures for the first 11 days of March and for the last 10 days of March.

e. What do the range and interquartile range tell you about the variability and spread of the data set?

Guiding Questions

The lower and upper quartiles are sometimes referred to as the median of the bottom half and the median of the top half of the data set. Why does that make sense?
If a data set has a big range, what does that tell you about the data?
If a data set has a small interquartile range, then what does that tell you about the data?
Why would knowing the interquartiles of a data set be helpful?
Describe variability and spread in your own words.

Notes

This Anchor Problem uses the paper strips from Lesson 6. If the strips were saved, then hand these back out to students. If not, then have students recreate them using the template Number strips. These strips may also be used again in Lessons 11 and 12, when students create and analyze box plots. It is helpful to compare the equal quartiles from the paper fold to the varying lengths of the box and whiskers in a box plot (MP.5).
A common summary of a data set is called a five-number summary of the data. This includes the minimum value, the lower quartile, the median, the upper quartile, and the maximum value.

Anchor Problems - Problem 2

Two brands of chips advertise the same serving size and approximate number of chips in the bag. You count the number of chips in a sample of 12 bags for each brand and record the data below.

Brand X:
36 38 38 38 40 42 42 44 44 45 48 49

Brand Y:
39 39 39 39 40 40 40 40 40 41 41 43

Which brand has less variability in the number of chips per bag? Justify your answer using data from the set.

Anchor Problems - Problem 3

Three dot plots are shown below.

Use the information shared below to determine which dot plot matches the situation.

a. You know the median of the data set is 4. Can you determine which dot plot represents the data set? Why or why not?

b. You also know the range of the data set is 6. Now can you determine which dot plot represents the data set? Why or why not?

c. You determine that the interquartile range of the data set is 4. Does this new information help you narrow in on which dot plot represents the data set?

d. For the other two dot plots, determine the lower quartile, the upper quartile, and the interquartile range of the data set.

Problem Set

View Problem Set

Target Task

The dot plot below represents salaries, in thousands of dollars, of students graduating with a Master’s degree from a graduate school.

a. Find the lower quartile, median, upper quartile, range, and interquartile range of salaries.

b. Explain how the interquartile range helps you understand the spread of the data set.